Find a subset of the vectors that forms a basis for the space spanned by the vectors, then express each vector that is not in the basis as a linear combination of the basis vectors. V₁=(1,0,1,1), V2=(-3,3,4,3), v3 = (5,3,12,11), V4 = (-11,3,-4,-5) OV1, V3, V4 form the basis; V2=5v1 +V3+7V4 V2, V3, V4 form the basis; V₁ = 3V2 + 2V3 + 3V4 V₁ V2 form the basis; V3 8V1+V2, V4-8V1+V2 OV1, V2, V4 form the basis; V3=-8v1+V2 + 2V4 OV1 V2 V3 form the basis; V4 = 8V1+V2 + 3V3
Find a subset of the vectors that forms a basis for the space spanned by the vectors, then express each vector that is not in the basis as a linear combination of the basis vectors. V₁=(1,0,1,1), V2=(-3,3,4,3), v3 = (5,3,12,11), V4 = (-11,3,-4,-5) OV1, V3, V4 form the basis; V2=5v1 +V3+7V4 V2, V3, V4 form the basis; V₁ = 3V2 + 2V3 + 3V4 V₁ V2 form the basis; V3 8V1+V2, V4-8V1+V2 OV1, V2, V4 form the basis; V3=-8v1+V2 + 2V4 OV1 V2 V3 form the basis; V4 = 8V1+V2 + 3V3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Find a subset of the vectors that forms a basis for the space spanned by the vectors, then express each vector that is not in the basis as
a linear combination of the basis vectors.
V₁ =(1,0,1,1), V₂ = (-3,3,4,3), V3 = (5,3,12,11), V4 = (-11,3,-4,-5)
V1, V3, V4 form the basis; V2 = 5v1 +V3+7V4
V2, V3, V4 form the basis; V₁ = 3V2 + 2V3 + 3V4
V1, V2 form the basis; V3 = 8V1+V2, V4=-8V1+V2
V1, V2. V4 form the basis; V3=-8v1 + V2 + 2V4
○ V1, V2, V3 form the basis; V4 = 8V1+V2 + 3V3
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